Simplify ( square root of x-4)^2

${(\sqrt{x} - 4)}^{2}$

Step 1

Rewrite ${(\sqrt{x} - 4)}^{2}$ as $(\sqrt{x} - 4) (\sqrt{x} - 4)$ .

$(\sqrt{x} - 4) (\sqrt{x} - 4)$

Step 2

Expand $(\sqrt{x} - 4) (\sqrt{x} - 4)$ using the FOIL Method.

Apply the distributive property.

$\sqrt{x} (\sqrt{x} - 4) - 4 (\sqrt{x} - 4)$

Apply the distributive property.

$\sqrt{x} \sqrt{x} + \sqrt{x} \cdot - 4 - 4 (\sqrt{x} - 4)$

Apply the distributive property.

$\sqrt{x} \sqrt{x} + \sqrt{x} \cdot - 4 - 4 \sqrt{x} - 4 \cdot - 4$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $\sqrt{x} \sqrt{x}$ .

Raise $\sqrt{x}$ to the power of $1$ .

${\sqrt{x}}^{1} \sqrt{x} + \sqrt{x} \cdot - 4 - 4 \sqrt{x} - 4 \cdot - 4$

Raise $\sqrt{x}$ to the power of $1$ .

${\sqrt{x}}^{1} {\sqrt{x}}^{1} + \sqrt{x} \cdot - 4 - 4 \sqrt{x} - 4 \cdot - 4$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${\sqrt{x}}^{1 + 1} + \sqrt{x} \cdot - 4 - 4 \sqrt{x} - 4 \cdot - 4$

Add $1$ and $1$ .

${\sqrt{x}}^{2} + \sqrt{x} \cdot - 4 - 4 \sqrt{x} - 4 \cdot - 4$

Rewrite ${\sqrt{x}}^{2}$ as $x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

${(x^{\frac{1}{2}})}^{2} + \sqrt{x} \cdot - 4 - 4 \sqrt{x} - 4 \cdot - 4$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{\frac{1}{2} \cdot 2} + \sqrt{x} \cdot - 4 - 4 \sqrt{x} - 4 \cdot - 4$

Combine $\frac{1}{2}$ and $2$ .

$x^{\frac{2}{2}} + \sqrt{x} \cdot - 4 - 4 \sqrt{x} - 4 \cdot - 4$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{\frac{2}{2}} + \sqrt{x} \cdot - 4 - 4 \sqrt{x} - 4 \cdot - 4$

Rewrite the expression.

$x^{1} + \sqrt{x} \cdot - 4 - 4 \sqrt{x} - 4 \cdot - 4$

Simplify.

$x + \sqrt{x} \cdot - 4 - 4 \sqrt{x} - 4 \cdot - 4$

Move $- 4$ to the left of $\sqrt{x}$ .

$x - 4 \cdot \sqrt{x} - 4 \sqrt{x} - 4 \cdot - 4$

Multiply $- 4$ by $- 4$ .

$x - 4 \sqrt{x} - 4 \sqrt{x} + 16$

Subtract $4 \sqrt{x}$ from $- 4 \sqrt{x}$ .

$x - 8 \sqrt{x} + 16$